I was unsure about whether to include brackets or parentheses when writing interval notion. I really appreciate your clarity on that. Just got a 100 on my math quiz! Thanks! :)
Thank you so much, I thought I would fail my math test but this explained the things i was confused about. I'm ready to go into my math test :) thank you so much.
With all due respect, I disagree that the answer to the question, "Intervals where a function increases" is (-infty, -2) union (1,infty) for one reason: that set is not an interval. An interval by definition has no gaps, punctures or holes. Because the question wants intervals, the correct answer is (-infty, -2), (1, infty). Those are intervals. Not every union of intervals is an interval, like your example. If the question was list the set of values where the function is increasing, then I agree with your answer: It is the collection of all values where the function is increasing, but to be clear, that collection is not an interval. In fact, if you had the union of two intervals that overlapped, that will be an interval! We can show that it is a necessary and sufficient condition. The only reason I'm posting this is because I tutor math and often the teacher's use weassign. I see students get this question wrong when they put union of intervals, and then the teachers don't have any justification for it, and I've seen them tell the students, "It's probably just a bug." But no, it's not a bug, and I'm tired of seeing teacher's claim that union of intervals, like your example, is an interval. This is as wrong to me as 1 + 1 = 5 using the addition operator on the set of real numbers. In short, your answer is a set, not an interval (although, just to cover my butt, an interval is a special kind of sets. So, all intervals are sets, but not all sets are intervals, and yours is an example). Cheers.
That constant interval you wrote should be in brackets. [-2, 1] You do need to include those points. To clarify, that constant interval on the graph can be written as the piecewise function: f(x) = { -1 if -2 less than or equal to x less than or equal to 1}. If you evaluate that function at -2 the output would be -1. Similarly if you plugged in -1.999 the output would be -1. You do need to include -2 and 1, there should be brackets.
Thanks for the videos. I plugged "U" as you mentioned and I got it wrong but I think that was my fault cause the answer should have been with "," as mentioned in my homework instructions. The answer should have been (-oo,-4),(4,oo) NOT (-oo,-4)U(4,oo) .
I was unsure about whether to include brackets or parentheses when writing interval notion. I really appreciate your clarity on that. Just got a 100 on my math quiz! Thanks! :)
Great job Val! Glad my video helped you with your quiz!
For me you are my favorite teacher , so great many thx for all infos
Thank you so much, I thought I would fail my math test but this explained the things i was confused about. I'm ready to go into my math test :) thank you so much.
Glad it helped!
Great video!
Thank you this helped a lot
Is it only when finding the domain and range where it includes the brackets?
This video I did might help you understand it more Mohammed Interval Notation (What is It?) th-cam.com/video/lCj3M6kZX5w/w-d-xo.html
Thanks Mario!
You’re welcome.
With all due respect, I disagree that the answer to the question, "Intervals where a function increases" is (-infty, -2) union (1,infty) for one reason: that set is not an interval. An interval by definition has no gaps, punctures or holes. Because the question wants intervals, the correct answer is (-infty, -2), (1, infty). Those are intervals. Not every union of intervals is an interval, like your example. If the question was list the set of values where the function is increasing, then I agree with your answer: It is the collection of all values where the function is increasing, but to be clear, that collection is not an interval. In fact, if you had the union of two intervals that overlapped, that will be an interval! We can show that it is a necessary and sufficient condition. The only reason I'm posting this is because I tutor math and often the teacher's use weassign. I see students get this question wrong when they put union of intervals, and then the teachers don't have any justification for it, and I've seen them tell the students, "It's probably just a bug." But no, it's not a bug, and I'm tired of seeing teacher's claim that union of intervals, like your example, is an interval. This is as wrong to me as 1 + 1 = 5 using the addition operator on the set of real numbers. In short, your answer is a set, not an interval (although, just to cover my butt, an interval is a special kind of sets. So, all intervals are sets, but not all sets are intervals, and yours is an example). Cheers.
weassign should be WebAssign.
I had webassign hw and it was so bad. It made me more stupid
he really confused me when he put -3. Thanks for this. I thought I was the only one
That constant interval you wrote should be in brackets. [-2, 1] You do need to include those points. To clarify, that constant interval on the graph can be written as the piecewise function: f(x) = { -1 if -2 less than or equal to x less than or equal to 1}. If you evaluate that function at -2 the output would be -1. Similarly if you plugged in -1.999 the output would be -1. You do need to include -2 and 1, there should be brackets.
Thanks for the videos. I plugged "U" as you mentioned and I got it wrong but I think that was my fault cause the answer should have been with "," as mentioned in my homework instructions. The answer should have been (-oo,-4),(4,oo) NOT (-oo,-4)U(4,oo) .
you have no idea how much frustration this saved me for my hw. thank you so much
Pearson be like that😭
example 2 is incorrect :)
Union notation should be avoided at all times. The word "and" will suffice. That is calc 101 and you failed